Applied Physics Topics 2

Dr Andrey VarvinskiyConsultant Anaesthetist

Torbay Hospital, UK

EDAIC Paper B Lead and Examiner

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Conflict of interest declarationWHAT DECLARATION

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Other Flight and hotel funded by ESA

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TOPICS 2Gas Laws

Other Laws: Dalton, Avogadro

Critical temperature

Critical pressure

Solubility

Diffusion

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Boyle’s Law(Boyle-Mariotte law)

PV=k1

For a fixed amount of an ideal gas kept at a fixed T, pressure and volume are inversely proportional (while one doubles, the other halves)

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Cylinder contentAir,O2,Helium: by pressure gauge asP is proportional to V

N2O and CO2: by weight. Liquified under Pressure

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Application of Boyle’s Lawfor calculating a content of a cylinder

p1 x V1 = p2 x V2

P1 = Gauge pressure of cylinder

V1 = Physical volume of cylinder

P2 = Atmospheric pressure

V2 =Actual amount of gas stored in the cylinder

For CD O2 cylinder :

230 x 2 = 1 x V2 = 460 L

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Charles Law Law of Volumes

V/T = k2

Constant pressure

Gases expand when heated

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Charles Law Practical Application

Heat loss from the body - air next to the body surface gets warmer and moves up

Patient loses heat

Important in paediatrics

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3rd Perfect Gas Law

P/T = k3

Constant volumethe absolute pressure of gas varies directly to its absolute temperature

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3rd Perfect Gas Law Practical Application

Medical gases are in cylinders at constant volume and high pressures (138 Bar in a full O2 cylinder)

At high T, pressure will rise causing explosions

Molybdenum steel can withstand pressures to 210 Bar. Weakening of metal in damaged cylinders are at a greater risk of explosion due to rise in temperature.

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The Universal Gas Law

Combining all the gas laws together yields animportant equation: the universal or ideal gaslaw.

PV = nRT P – Pressure of gasV - Volume

n = the number of moles of the gasT – Temperature of gas

R = the universal gas constant

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Standard Temperature and Pressure (s.t.p.)

Volumes of gases are affected by T and P hence there is a need to specify those

And to correct results

273.15 K (00 C)

101.325 kPa

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Dalton's Law Of Partial Pressures

in a mixture of gases the pressure exerted by each gas is equal to the pressure which would be exerted if that gas alone was present

PressureTotal = Pressure1 + Pressure2 ...Pressuren

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Dalton's Law Practical ApplicationIn anaesthesia the partial

pressures of gases in a mixture are of interest

By applying Boyle’s and Dalton’s law the partial pressure of a gas in a mixture is obtained by multiplying the total pressure by the fractional concentration of the gas.

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Dalton's Law Practical ApplicationIn a mixture of gases where

0.05% - CO2, 20.9%- O2 and

78.1% - N2

If the total Pressure is 100kPa the pCO2 – 0.05kPa, pO2-20.9kPA, pN2 – 78.1kPa

If the total pressure doubles (200kPa) then the partial pressure of each gas doubles.

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Avogadro's Hypothesis

equal volumes of gases at the same temperature and pressure contain equal numbers of molecules

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Avogadro's Hypothesis

Because the molecular weights of gases differ, there will be a different mass of any gas in a given volume at the same temperature and pressure

Therefore it is more convenient to express a quantity of a gas in terms of the number of molecules, rather than in terms of mass.

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AVAGADRO and the MOLE

A MOLE is the quantity of a substance containing the same number of particles as there are atoms in 0.012kg of carbon12

There are 6.022 x 1023 atoms in 12 g of carbon 12. This is called Avagadro’s Number

One mole of any gas at s.t.p. occupies 22.4litres

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The MoleTHUS:

2g of Hydrogen

32g of Oxygen

44g of Carbon DioxideAll occupy 22.4 litres at s.t.p

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Ideal Gas LawThe most significant consequence of Avogadro's law

is that the ideal gas constant has the same value for all gases

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Critical TemperatureT above which a substance

cannot be liquefied however much pressure is applied N2O: 36.5C O2: -119C CO2: 31C

“Gas” applies to a substance above its CT

“Vapour” is for a substance below its CT

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Critical Pressure Pressure needed to liquefy the gas at its critical temp

N2O - 72 bar

O2 – 50 bar

CO2 – 73 bar

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Filling Ratio mass of gas in a

cylinder/mass of water which would fill the cylinder

For N2O it’s 0.75 in the UK, hotter climates – 0.67

Necessary to prevent explosion in case of rise in temp

So N2O cylinder contains a mixture of liquid and vapour

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Solubility and Henry’s Law

At particular T the amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid

different gases have different solubilities

Overall: solubility of a gas depends on partial pressure, temp, gas and liquid concerned

↑temp of liquid =>↓dissolved gas

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Partition Coefficients

ratio of amount of a substance present in one phase as compared with another

two phases must be of equal volume, specified temperature in equilibrium

Tension is often used in place of partial pressure for gases in solution (don’t mix with surface tension)

Could be applied to 2 different liquids (blood-gas, oil- gas)

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DiffusionMovement of a substance from an area of high

concentration to one of low concentration due to spontaneous random movement of its constituent particles

Not an active process as no energy required

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Fick’s law of diffusionrate of diffusion of a substance

across a membrane is proportional its concentration gradient and inversely proportional to the tissue thickness

diffusion of gas across a membrane or into or out of a liquid is proportional to the gas’s solubility in the liquid

CO2is more soluble than O2 and so diffuses more rapidly across the alveolar membrane

N2O more soluble than N2 - can diffuse into and expand closed cavities

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Graham's LawEffect of molecular size

Rate of diffusion of a gas is inversely proportional to the square root of the molecular weight

Only applies to simple models and is inaccurate when dealing with complex biological membranes

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Diffusion Summary

Diffusion is proportional to the tension gradient

D depends on area and thickness of membrane

D is affected by molecular size (larger diffuse less rapidly)

Liquids diffuse less rapidly than gases

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QUESTIONS?

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